Based on your map I have a few suggestions:
1) Instead of taking the autobahns between Salzburg and Mieders (and Mieders and Neuschwanstein) use the German Alpenstrasse. It is a beautiful drive. It's a lot slower but it's worth it. Also, the twists and turns and stops are ideal for the break-in period. You will have a chance to open it up later in the trip.
2) In my mind Zurich is just another big city. Perhaps someone else on the forum can suggest an area of northern Switzerland that is prettier. You might head up to Schaffhausen, where the Rhine Falls are located, as an option. Though neither Zurich nor Scaffhausen will equal most of the rest of Switzerland in natural beauty.
3) Instead of going up the E5 to Strasbourg, head into Alsace, France and see Mulhouse, Colmar and Riquewihr. They are all pretty cities/towns and worth an hour or two each.
4) Downtown Nuremberg is worth a stop. It's also got a lot of pre-WWII sites that are interesting if you are a WWII buff. There is also a Documentation Center which reviews the build-up of the Nazi party.
5) When heading from Heidelberg to Nurburgring take the road from Koblenz to Cochem which is alongside the Mosel River. There are lots of cute little towns, castles, vineyards to enjoy.
6) Hamburg is a long way out of your way. The city does have a pretty little lake but otherwise is just another modern city. The Miniature Wonderland does appear to be a worthwhile site and may make the extra 12 hours or so of travel worthwhile.
May should be a beautiful time to travel. The flower boxes decorating the alpine chalets should be in bloom. If you have good weather it should be a great trip.